Aim: How do we find the probability of an event? Outcome Any one of the possible results of an event. Example: Landing on 1, 2, 3, 4, 5 or 6 when a die.

Aim: How do we find the probability of an event?

OutcomeAny one of the possible results of an event.

Example: Landing on 1, 2, 3, 4, 5 or 6 when a die is rolled.

Example: Rolling a die

EventA situation involving chance that has more than one possible outcome.

Theoretical Probability

The likelihood a specific outcome will occur.


A spinner has four equal sections colored yellow, blue, green and red. What are the chances of landing on red with a single spin?

Probability (P) =the number of favorable outcomes

the number of possible outcomes

Formula for probability:

P (red) =16


A single six-sided die is rolled.What is the probability of rolling a 1, 2, 3, 4, 5 or 6?

number of favorable outcomes

number of possible outcomes

P (1) =

P (6) =

P (5) =

P (4) =

P (3) =

P (2) =

e.g.,

16

16

16

16

16

16


P (Even) = =

A single six-sided die is rolled. What is the probability of rolling an even number?

Number of sides with even numbers

Total number of sides

P (Odd) = =Number of sides with odd numbers


P (Not 2 or 3) = =Number of sides without a 2 or 3


36

36

46

= 1 2

= 1 2

= 2 3


P (red) =

P (blue) =

P (green) =

P(yellow) =

A pail contains 8 red marbles, 5 blue marbles, 6 green marbles and 3 yellow marbles. Find the probability for the following events if a single marble is chosen from the pail.

522

622

822

322

= 3 11

= 4 11


A pail contains 8 red marbles, 5 blue marbles, 6 green marbles and 3 yellow marbles. Find the probability for the following events if a single marble is chosen from the pail.

P (not red) =

P (red or yellow) =

P (blue or green) =

P(black) =022

= 14 22

8+322

5 + 6+ 3 22

= 11 22

= 1 2

= 7 11

5+622

= 11 22

= 1 2


Practice1. What is the probability of choosing a purple marble from a jar containing three purple, two green and eight orange marbles?

2. If the letters in "probability" were placed in a hat, what would be the probability of choosing a "b" in a single draw?

= 3 13

= 2 11

3. If the letters in “Williams" were placed in a hat, what would be the probability of choosing a vowel in a single draw?

= 3 8


4) Kasim's Video Store has received a shipment of DVDs. The table below shows the number of each type of DVD in the shipment. (2008)

Kasim selects a DVD at random from the shipment. What is the probability that he chooses a western?

DVD ShipmentType Number of DVDsAction 12Science Fiction 3Comedy 6Western 9


5) Rachel has 5 silver bracelets and 2 gold bracelets in her jewelry box. Rachel randomly picks on bracelet. Which statement best describes which bracelet she will probably pick? (2007)

a) She probably will pick a gold bracelet.

b) She definitely will pick a gold bracelet.

c) She probably will pick a silver bracelet.

d) She definitely will pick a silver bracelet.


6) Veronica has a box that contains 24 pictures of her family, 6 pictures of her dog, and 12 pictures of her friends. Veronica randomly chooses one picture from the box. Which statement best describes what will likely occur? (2008)

a) She will definitely pick a picture of her family.

b) She will most likely pick a picture of her family.

c) She is equally likely to pick a picture of her family or of her dog.

d) She is equally likely to pick a picture of her family, of her dog or of her friends.


Theoretical probability is what will happen in an ideal situation.

Experimental probability is what happens when you actually perform the event


Find the theoretical probability for each event.

P (red)

P (orange)

P (purple)

P (yellow)

P (green)

= 1 5

= 1 5

= 1 5

= 1 5

= 1 5


P (red)

P (orange)

P (purple)

P (yellow)

P (green)

Find the experimental probability for each event. Using your data.

Compare the results of the theoretical probability with the results of the experimental probability. What do you notice?

Aim: How do we find the probability of an event?EXAMPLE 1

You roll a number cube 100 times. Your results are given in the table below.

1. Find the experimental probability of rolling a 6.

2. Find the theoretical probability of rolling a 6.



3.Find the experimental probability of rolling a number greater than 3.

4. Find the theoretical probability of rolling a number greater than 3.



5. Find the experimental probability of rolling a number less than or equal to 2.

6. Find the theoretical probability of rolling a number less than or equal to 2.



7. What is the experimental probability of rolling a 3?

8. About how many times would you expect to roll a 3, if you roll the number cube 500 times?


1) The table below shows the bowling scores of 125 students.

a) What is the experimental probability that the next student who bowls will have a score that is 126 or more? (2007)b) What is the experimental probability that the next student who bowls will have a score that is 99 or less?

Bowling Scores

Students Number of Students

Under 100 28

100-125 52

126-150 30

151 and up 15


2) A number cube is a cube with each side labeled with a number 1 through 6. Debbie rolled a number cube 60 times. The tally table below shows the number of times each number, 1 through 6, appeared?(2008)

Before her experiment, Debbie expected each number on the cube to appear an equal number of times. Which statement best compares the results of Debbie's rolls with her expectations? a) Debbie rolled more 5s than expected. b) Debbie rolled fewer 4s than expected. c) Debbie rolled more 3s than expected. d) Debbie rolled fewer 2s than expected.

Rolling a Number Cube Number on the Cube Number of Rolls 1 2 3 4 5 6


(2009)3)


4) A company manufactures buttons. A quality control inspector finds 2 defective buttons in a batch of 300. About how many buttons would you expect to be defective in a shipment of 20,000 buttons?

You could expect about 133 buttons in a shipment of 20,000 to be defective.

P(defective buttons) =defective buttons =all the buttons

x___ 20,000

2 =

300300x = 40000 300 300 x = 133


6) You randomly draw a marble from a bag of 200 marbles. You record its color and replace it. Use the results to estimate the number of marbles in the bag that are yellow.

Red Yellow Blue Green9 10 14 7


1. Create a table to store your experimental data.

2. Roll your cube or spin your spinner 50 times. Each person in the group should get a chance. Use tally's to record your data in the table.

6. Use the results of your experiment to predict how many times you would get each outcome if you performed the event 200 times.

3. What is the probability of rolling or spinning a number greater than 4?

4. What is the probability of rolling or spinning a number less than or equal to 3?

5. What is the probability of rolling or spinning a 1 or 5?

Number 1 2 3 4 5 6Rolls/Spins

Group Work

Aim: How do we find the probability of an event? Outcome Any one of the possible results of an event. Example: Landing on 1, 2, 3, 4, 5 or 6 when a die.

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